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AD-A140,081 DEVELOPMENT OF AN INTERFEROMETN C TECHNIQUE FOR f/ NEDUCTION OF BACKGROUND NADIATION AT 10 MICROMETENS(U) ANIZONA UNIV TUCSON DEPT OF FHYSICS 1984

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I THE UNIVERSITY

09"r-TUcSON, ARIZONA 85721 USA

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COLLEGE OF ARTS AND SCIENCES

FACULTY OF SCIENCE

1.

Introduction

DEPARTMENT OF PHYSICS

" BUIL.DING #81

" This report concerns tbe final status of the ONR contract

-no. NOOI4-8 -Cz O79 entitled"Development of an Interferometric

Tech-nique for Reduction of Background Radiation at 10 M , "

The purpose of the proposed instrument was to improve the detecta-bility of a background limited source in the atmospheric ,window' from 8 to 12 gm. Such an improvement would be possible if the photons arising

from the source and background could be discriminated interferometrical-ly such that the "desiredo signal photons were preferentialinterferometrical-ly detected. This has been the motivating idea of the devices considered.

00 A great deal of progress toward fulfilling the particular design

Q requirements of the proposed instrument has been made, and this is the subject of Section 2. However, in the process of calculating the

in-0

uncovered (see Section 3.5 for a detailed description). Variations of the parameters involved have not succeeded in circumventing the problem. Unfortunately, the consequence of this problem is that improvement in

the signal to noise ratio is not attainable with this instrument.

Further study covered a wide spectrum of alternative methods of achieving our initial goals. In the formal analysis of all designs Sconsidered, it became apparent that no improvement in the ratio of detected signal photons to detected background photons could to be expected using interferometric reduction. Section 2.6 presents an ex-planation of the inability to detect signal photons preferentially over background photons. This argument is quite general and can be applied to any of the designs considered.

However, one of the ideas considered was found to have merit in

certain classes of background limited detection. This mode of operation will detect signal and background photons alike and, therefore, the statistical fluctuations of the background will still limit the signal

to noise ratio. The salient feature of this device is the ability to :>_ measure and subtract an extended, nonuniform background intensity from

C1_ an unresolved (or point-like) signal intensity. The usual technique

C) must measure the background beyond the source and extrapolate and/or

C-D interpolate to the region occupied by the desired signal.

L This method of background compensation is fundamentally different

-. J

-A- from the originally proposed technique. Since the original method would have relied on Interferometric cancellation of the background field, it

2 shall be referred to as "background amplitude compensation." The new device uses interferometric techniques to measure the background in the

line of sight and then subtracts the background from the signal after

detection of the field has occurred. This latter technique will thefkz

fore be called "background intensity compensation."

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-Although the original proposal did not address background intensity compensation, approval for further study of this technique was granted at the time of the last extension. A description of the theory of

operaion and results of testing of this technique at a wavelength of

6328 A are provided in Section 3.

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2. Background Aaplitude Compensation

This section shall deal with the various design aspects of the originally proposed device. The subsections which follow are in roughly chronological order, although some projects were carried out simul-taneously.

2.1. Regular Array Grating

The instrument design considered at the start of the contract period is depicted in Figure 1. A problem with the intended grating was discovered shortly before the start of the contract period. In the mask plane behind the regular array phase grating, the peaks for the distri-bution of the desired signal and background amplitudes were found to occupy the same region, i.e., the region where the background amplitude was to be blocked. Previous tests with 3 mm microwaves did not measure the signal while the background blocking mask was in place, and this problem went undiscovered until the signal diffraction pattern in this plane was calculated analytically. Further tests with the 3 mm micro-wave equipment confirmed the results of this analysis.

2.2. Irregular Array Grating

Alternatives to the initial design were considered when the problem described in Section 2.1 was realized. It was found that, by permitting some of the grating elements to be twice as wide as normal, the peaks of the background and signal diffraction patterns in the mask plane were very thoroughly separated. In this case, the signal refers to that part of the image field which overlaps the double-width grating elements. An irregular grating of this sort can be extended into a two-dimensional array by forming a product of linear arrays. The grating pattern which was found best suited to the proposed application is shown in Figure 2. The light elements produce a phase shift of 180 degrees relative to the dark elements. This pattern provides for eight separate regions in the field where background compensation would occur.

2.3. 3 mm Microwave Tests

A plexiglass irregular array phase grating was constructed to test the idea presented in Section 2.2. A line grating was used rather than the two-dimensional grating in order to simplify construction and detec-tor positioning. The irregular grating replaced the previous regular grating in the 3 mm microwave setup. Results of measurements in the mask plane were in good agreement with the numerical diffraction calcu-lations as shown in Figure 3. Differences between the measured

inten-sities and the theoretical values are attributable to the aberrations of

the optical elements and the departure of the microwave source from an ideal point source.

3

Telescope Focal Plane

Entrance Pupil 2nd Focal Plane

onto Optics to Image I'st Grating onto Complementary 2nd Gratingi Regular Array Reflective Grating (2nd) 3rd Focal Plane p -Background Blocking Mask 4th Focal Plane and Detector Figure 1 Basic Design of Initially Proposed Instrument

Figure 2 Irregular Array Grating

The dark elements shift the phase of the transmitted wavefront by 1800 relative to the light elements. The desired signal would be measured at the eight "double-size" squares in the central region.

2.4. Optical Elements

Figure 4 gives a schematic layout of the planned optical design. For the sake of clarity, the figure does not show certain folding mir-rors which would have been included to minimize the volume of the dewar required for low temperature operation. Except for the achromatic phase shifters, all transparent optical elements were to be made of germanium, which has the advantages of low absorption and a nearly constant refrac-tive index within the 8 to 12 um atmospheric window. Due to the unusu-ally high index of refraction of germanium, - 4, the utility of the design is very dependent on antireflection coatings. Coatings were found to be commercially available which reduced the air-germanium reflection from 36% to < 1% in the full range of the atmospheric window.

2.4.1. Achromatic Phase Shifters

A crucial aspect of the instrument design was devising a means of producing a 1800 phase shift between alternate grating elements over the full band of interest. A modified Mach-Zehnder interferometer with reflective gratings as beamsplitters was used to divide the image plane into two beams which could be phase shifted with respect to each other. This phase shift can be made nearly achromatic by inserting, into the

two beams, a carefully selected combination of transparent plates made of different materials. Upon further study of this idea, it was found

that a slight difference in the air path length between the two legs, coupled with a single plate, could produce an achromatic phase shift. Many materials were considered, with the optimum choice found to be cesium iodide (CsI). For a plate thickness of 596 um and an air gap of 445 um, the phase shift in the wavelength range of 8-14 um varies from 176.90 to 183.10. The sensitivity of the phase shift to a change in plate thickness was an important design consideration. In the case of CsI, a 10 um error in the ideal plate thickness, with the air path dif-ference adjusted to minimize the effect of the error, changes the phase variation from 6.20 to 6.80. The use of this technique to provide an achromatic relative phase shift could be useful in a variety of

inter-ferometric systems.

2.4.2. Grating Imaging

In order for the Mach-Zehnder system to represent a simple phase grating adequately, it is essential that the elements of the first reflective grating be accurately mapped to the corresponding elements of the second grating. This requirement was found to impose much more stringent demands on the optics than was typical for the rest of the

system.

Several designs were considered before one of sufficient quality was found. In order to evaluate a specific design, a computer ray tracing code (ACCOS-V) was used. Rays were initiated at representative points on the first grating, and then directed to cover the pupil uni-formly. After the trace was carried out to the second grating surface, the spot diagrams resulting from these ray bundles could be analyzed.

7

The design which gave the best imaging properties was also quite

simple (see Figure 4).

The two reflective gratings lie in the same

physical plane of a cube germanium beamsplitter.

Although the gratings

are tipped at

relative to the optical axis, the effect of the

*

germanium prism is to reimage this surface to an angle of only

This considerably reduces the aberration near the edges of the imaging

field. Plano convex germanium field lenses which are in optical contact

with the cube beamsplitter image the objective onto the spherical

mir-rors (at E2).

_{The two plates in these two divided beams are the CsI}

phase shifters.

Although only one plate is required in principle, two

were to be used in order to balance the reflective losses of the two

legs and to allow for thicker plates.

The difference in the thickness

of the two plates must equal the thickness of the single plate described

in Section 2.4.1.

Note

that, since the gratings lie next to each other,

they are rectangular in order to minimize the object and image

separa-tion.

For the arrangement shown, the r.m.s. spot diameter from the

geometric ray trace calculations varies from 13 to 35

um

across the

full

field of the grating. This is quite acceptable, considering that the

diffraction-limited spot size at a 10

pmn

wavelength is 35

pim

for

this

f/3.5 system.

The combined effects of diffraction and aberration

are,

therefore, expected to produce an upper limit spot size of

50

uim,

acceptably small compared to the grating element size of 450

Jim.

2.5.

Computer Modeling

Soon after the idea for the irregular grating was proposed, the

diffraction patterns due to both signal and background sources were

calculated numerically. The plane in which this diffracted amplitude

was initially evaluated was located at the background blocking mask (E3

in Figure 4).

It seemed clear at this point that, since the peak

amplitude due to the signal did not overlap the peak due to the

back-ground, the signal to noise level after this mask plane would be

im-proved.

Extending the numerical calculations to the final image plane

was to be the test of this expectation.

The necessary calculations

turned out to be quite tedious, and a considerable amount of time and

effort was spent before the model results were reliable. Unfortunately,

the outcome did not confirm the intuitive reasoning presented above.

To simulate a uniform background, fifty randomly distributed point

sources were placed in the plane of the objective. The signal source

was simulated by a plane wave at the objective which could be tipped at

any desired angle.

The resultant amplitudes were calculated in the

final image plane with the blocking mask both in place and absent.

The

background distribution was quite uniform in this plane when the

block-ing mask was removed.

However, when the blocking mask was in place, the

final image plane distribution became peaked at the eight locations

where the double-size grating elements were imaged, corresponding to the

intended signal regions.

To the expected precision of the calculation,

no increase in the signal to background ratio was found upon putting the

blocking mask

in

place.

The effect of changing parameters in the grating and mask was assessed next. By making the grating larger, with a greater number of

small elements on the periphery, the background distribution in the mask plane became more sharply peaked. However, the amplitude level which is

not masked still led to peaks of the same size in the final image plane. If the mask was designed to block off more background, the peaks in the final image plane resulting from both the signal and background became

wider (as expected from the smaller mask aperture), but their amplitude ratio remained unchanged.

2.6. Inability to Distinguish Background and Signal Photons A variety of alternate designs, aimed at achieving the initial goals of the contract, were considered. In all cases, the background photons were eliminated by the same factor as were the signal photons, with no gain in the signal to noise ratio. This section gives a general explanation for this result.

Huygen's principle states that every point of an arbitrary electro-magnetic wavefront can be regarded as the origin of a point source, and the superposition of all these point sources is, in all respects, equiv-alent to the original wavefront. In addition, from the principle of superposition, the amplitude of an electromagnetic wave at a chosen point in space will equal the sum of amplitudes arising from all point sources representing the wave. The point sources which represent the wave can be selected on any wavefront and, therefore, are not restricted to any spatial region as the original point source may have been.

Now consider a background amplitude compensator which is to be placed in front of an intensity detector D. We require this device to pass photons which originate at some point S preferentially over those which originate on a surface B which lies between S and D (see Fig-ure 5). With this construction, any point b on B will intersect a point

on the wavefront of a photon generated at S. Therefore, the amplitude

due to this photon at D can be determined by considering separately the amplitude produced at D by every point on B. It follows that, if the compensator is to effect an overall reduction in amplitude at D for

background sources at B, then the amplitude at D due to S must be reduced by the same factor. This contradicts the requirement we have set for this device.

The argument above applies to a point-like signal and is clearly a special case of the proposed instument, which was to operate on an extended field and compensate for more than just a surface of background sources. However, one arrives at the same conclusion by applying the argument to all points in the region of the signal and all surfaces in the region of the background.

It is important to note that the argument that has been presented is only as strong as the starting points: Huygen's principle and the principle of superposition. For sufficiently stronq fields in a non-linear medium, non-linear superposition will not be entirely correct. How-ever, the practical applications for the type of instrument proposed

Background

Amplitude

Cornpensator

would almost certainly be directed toward weak fields in highly 1 media. In the case of Huygen's principle there is more room for s lation. Although this concept is well accepted, it is not dir

derivable from Maxwell's equations. The derivation of Fraunh

Fresnel diffraction given by Born and Wolf (1959) makes use of Hu

principle in a modified form which includes an "inclination fac This factor gives directional structure to each point making up a

front. Such structure is not expected from any realistic backg source, and the equivalence of a physical source and a "Huygen's source" seems questionable.

The objections raised above should demonstrate that this is n( a fully closed subject. However, since no counterexample to the ment presented has been found, it does not seem reasonable to cor

active study in this area.

Reference

M. Born ai, E. Wolf. 1959, "Principles of Optics," Pergamon Press,

3. Background Intensity Compensator

Among the alternate designs which were considered, one was found to

have interesting features even though it did not satisfy the initial objective. It appeared that this device would be capable of distin-guishing the detected intensities due to a point signal source and a nonuniform background. This idea was developed into a working model in the most recent extension period of this contract.

3.1. Principle of Operation

Figure 6 shows the basic optical design. The signal source is represented here by a plane wave tipped from the optical axis by an angle e. The entrance wavefront is then sampled by two matched aper-tures which are separated by a distance S. Objectives at the aperaper-tures focus this plane wave onto detectors D1 and D2. Before the detectors, the beams are combined by a 50/50 beamsplitter at B. For ideal align-ment of the system, the detector outputs will be:

=

c

cos

and

d

(e

where C is a constant intensity, X is the wavelength, and A is the phase difference of the optical paths from the first objective to DI and from the second objective to D1. The difference between these detector outputs will clearly depend on A, and will have a maximum magnitude when the term in parentheses is an integral multiple of w/2. If a background source is close enough to the objectives to avoid overlap of the two beam wavefronts on the detectors, then no interference between the beams can result. The time-averaged detected intensity due to such sources must then be the same for both detectors. Departures of the difference between these intensities from zero can only result from statistical fluctuations.

3.2. 6328 A Testing

Although the principle described in the previous section applies to the entire electromagnetic spectrum, the testing was conducted at an optical wavelength of 6328 A. The primary reason for this choice was the availability of equipment designed for this wavelength. In

13

-Figure 6

of Background Intensity-Compensator

addition, the use of a narrow band source eliminates the need for an achromatic phase shift between the two beams.

3.2.1. Optical Layout

Figure 7 schematically illustrates the arrangement of the test equipment. The two lasers used are 3 mW He-Ne lasers. A point source is simulated by projecting the beam from laser Li through a pinhole, thereby creating a Gaussian beam at the location of the compensator. The distance between the compensator and this pinhole was roughly 10 feet for all tests performed. Portions of this beam are separated by mirror M1 and prism 1 and mixed in the beamsplitter, B. The separation of the two beams is adjusted by translating M1 along the x-direction. Prism 1 can be moved in the y-direction to roughly balance the path lengths of the separate legs. In order to introduce small changes in the relative phase of the two beams easily, a piezoelectric "inchworm"1

was mounted to translate prism 2 in the y-direction.

After mixing the beams in the beamsplitter, they were focused onto the two detectors D1 and D2. Note that the objectives are on the detector sides of the beamsplitter. The specifications for these lenses are greatly simplified by placing them in the combined wavefronts. The signals detected by DI and D2 were then amplified and subtracted in a difference amplifier. The difference output due to the signal source

alone was maximized to align the two beams properly. The optical ele-ments used had a typical surface quality of X/10, and the phase varia-tion of the optimally aligned wavefronts over the selected apertures was less than x/4. Alignment of the apparatus was accomplished by rotating M2 and M3. Both mirrors could be rotated about two axes, one parallel and the other perpendicular to the horizontal plane.

Light from the second laser, L2, was expanded and directed onto a window coated with particulate scattering material. This simulated background source could be positioned at any location between the signal source and the interferometer structure. An irregular background was created by applying the particles to the window in streaks. The back-ground could be made even less uniform, both spatially and directional-ly, by aiming the specular reflection from the window into one or both legs of the interferometer.

3.2.2. Test Results

Several system configurations, using different beam separations, apertures and background characteristics, were tested. Results for all of the configurations were similar in that the intensity due to back-ground sources could be substantially subtracted from the desired

point-like signal intensity.

lInchworm Translators are a product of Burleigh Instruments, Fisher, New York.

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Laser L,

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Schematic Optical Lay-Out

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Beam I

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Beam,~,Chopper

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He-Ne

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of Background-Intensity Compensator

Fig-7.b)

of Dashed Box in Fiq-7.a

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Signal

From Chopper

From Di

Fig.-7.c)

From

DiElectronics

Followina Detectors

The magnitude of the difference output from the two detectors is a maximum for the signal source when the relative phase difference between the two beams is 0° or 1800. Since no means were provided to maintain this optimal phasing actively, the difference output would shift due to vibrations and temperature variations. For this reason, values of the difference output were measured by driving the inchworm while monitoring the peak-to-peak signal voltage on an oscilloscope. The balance between the detectors was then adjusted by centering this oscillating difference output about 0 V.

Table I summarizes the results of measurements made with both the background and signal sources in operation. The distance from the window, which was used to simulate the background source, to the front of the compensator is labeled here as W. The dimensions of the rectan-gular apertures which define the extent of the beams are given in the

column labeled Ap. The separation between the two beam centers is labeled d. The background to signal intensity ratio was measured by

blocking one beam and monitoring a single detector output while turning

on the background and signal sources separately; this output was

insen-sitive to the phasing of the two beams. The ratio was varied by atten-uating the signal or the background or by changing the properties of the background. The other intensities in the table are peak-to-peak values of the difference output. Since it is only necessary to compare inten-sities within the table, arbitrary units are used. For most cases, the signal level changed only slightly when the background source was turned on and off. In order to increase the magnitude of the background rela-tive to the signal, several measurements were made with the specular reflection from the scatter window entering one or both beams. Note that this caused the background to become extremely nonuniform. The peak-to-peak difference output in this case was comparable to the values

obtained in the nonspecular reflection source of background. The deci-sion was made to retain the original window, however, because the other windows produced larger wavefront aberrations in the signal source.

It should be mentioned that the balance of the two detectors was adjusted for each set of measurements. This was required since the beamsplitter had a dividing ratio of- 45/55 as opposed to the ideal 50/50. If the background intensity level of one beam is different from the other, the unbalanced splitting channels more light into one of the detectors. This effect could therefore be reduced either by improving the beamsplitter or by applying the system only to backgrounds with equal intensity in the beams. Alternatively, the balance could be actively adjusted to minimize the background level.

The noise sources arising in the electronics contributed an apparent intensity in the difference output of 0.06 ± 0.01 (see Table I), causing the measurements of the nonspecular background intensity to be systema-tically too large. In order to determine more accurately the reduction of the background source, a chopping system was introduced. The laser for the background source was placed behind a chopper-wheel, with an en-coder on the wheel serving as a reference signal for a lock-in amplifi-er. This technique greatly increased the dynamic range of the measure-ments of the difference output. Table II compares the background level due to a single detector output with that due to the difference output

Table II - Background Intensity Compensator Test Results

Lock-In Amplifier Output Reduction Background Single Detector On Difference Mode Factor

Specular reflection 102 0.20 510

in beam I only

Specular reflection 192 0.25 770

in beam 2 only

Diffuse scattering 1.12 0.0050 220

(specular reflection off)

for several cases. It was found that, after adjusting the balance of the detectors, the background was typically reduced by a factor of

several hundred while operating in the subtractive mode. The primary

limitations on further reduction were simply the "graininess" of the balance potentiometer and random fluctuations of the lock-in amplifier

output.

3.3. Applications

There already exist various methods for correcting a signal contam-inated by background radiation. These methods are based upon interpola-tion of the background superimposed on the source through measurements of the background in regions near the source. For a single detector system, this technique requires some type of scanning device. This can significantly reduce the time available to measure the signal, especial-ly when rapid changes in the background are occurring. Alternativeespecial-ly, a multi-detector system can be used in order to continually monitor the signal and surrounding background.

In using the method of background subtraction described here, one must considerably increase the complexity of the optical design over the conventional designs. The new design offers two primary features which, in some cases, may justify the added complexity. One advantage is the elimination of the hardware and processing required to estimate the background at the source from the surrounding background. The other advantage is quite unique to this design and relies on the spatial separation of the input beams. If the two beams corresponding to a

background source do not overlap on the detector, no interference be-tween the beams can occur. In this case, the background source can be arbitrarily nonuniform and the resulting detected intensities will be subtracted to the precision set by the quality of the beamsplitter.

The greatest limitation imposed on this design is the requirement for a point-like signal source. Nevertheless, several useful applica-tions exist for a device such as this. Radar systems which operate in the presence of a nonuniform background (such as varying weather conditions) could benefit by this technique. Microwave and radio commu-nication could be made less susceptible to interfering (or jamming) backgrounds. Note also that the power requirements of the source or the receiving aperture area could be reduced with sufficient subtraction of the background sources.

It is also possible that the principle would aid in detection or communication in the visible and infrared portions of the spectrum. In this case, careful consideration would be required of the effects of atmospheric turbulence on the signal detectability. None of the tests performed have addressed this problem. However, it is likely that active alignment techniques could compensate for such fluctuations if the individual apertures were small in comparison to the dominant scale length of wavefront aberrations introduced by turbulence.

4.

Concluding Remarks

It is clear that the most significant conclusion arising from this

study is the inability of the initially proposed instrument to increase

the detected signal to background ratio.

An extensive search has been

conducted for other types of instruments capable of detecting

signalI-photons preferentially over background signalI-photons; this search has been, to

date, unsuccessful.

Although the initially proposed instrument was found not to be

practicable, this result does represent newly acquired knowledge which

may be useful in other studies.

In addition, significant progress has

been made on the background intensity compensator.

The potential

appli-cations of this device are much more limited than those of the initial

instrument; however, this study has demonstrated that the background

intensity compensator, within the specified constraints, will function

in

the manner intended.